Scarhaven Keep by Joseph Smith Fletcher

When the great actor, Bassett Oliver, who was a martinet for punctuality, failed to turn up to a rehearsal which he himself had called, his business manager guessed that something had happened. It had. But it took more than one set of brains to discover the truth, and another set of very curious circumstances was mixed up in it. Copplestone, the young dramatist, helping to solve the mystery, found himself suddenly in love; and the solution and his happiness were discovered together.